feat(cgal): propagate Newton status + conditioning diagnostics into CGAL results

Follow-up to S2: surface the new NewtonResult diagnostics through the public
CGAL result types so callers of the high-level API see them too.

- Add `CGAL::Newton_status` (alias of conformallab::NewtonStatus) and three
  fields — `status`, `sparse_qr_fallback_used`, `min_ldlt_pivot` — to
  Conformal_map_result, Hyper_ideal_map_result and Circle_packing_result.
  (sparse_qr_fallback_used already existed on Conformal_map_result but was never
  populated; it is now wired through.)
- Map them from NewtonResult at all five entry points (euclidean / spherical /
  hyper_ideal / inversive_distance / cp_euclidean).
- Test: SingleTriangleConverges now asserts status == Converged and the
  diagnostics propagate.

Additive only — existing `converged`/`iterations`/`gradient_norm` semantics
unchanged. 301/301 CGAL tests pass.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

code/include/CGAL/Discrete_circle_packing.h

@@ -96,6 +96,9 @@ struct Default_cp_euclidean_traits<CGAL::Surface_mesh<typename K::Point_3>, K>
 Result of `discrete_circle_packing_euclidean`.  Carries face DOFs
 `ρ_f = log R_f` rather than the vertex DOFs of the classical modes.
 */
+/// Why the Newton solve terminated (re-exported from the solver; I1 audit).
+using Newton_status = ::conformallab::NewtonStatus;
+
 template <typename FT = double>
 struct Circle_packing_result
 {
@@ -108,6 +111,14 @@ struct Circle_packing_result
     FT   gradient_norm = FT(0);
     /// `true` iff `gradient_norm < gradient_tolerance` at exit.
     bool converged     = false;
+
+    /// Why the solve stopped: `Converged` / `MaxIterations` /
+    /// `LinearSolverFailed` / `LineSearchStalled`.
+    Newton_status status = Newton_status::MaxIterations;
+    /// `true` iff any Newton step fell back to SparseQR (gauge singularity).
+    bool sparse_qr_fallback_used = false;
+    /// Smallest `|Dᵢᵢ|` of the last LDLT (near-singularity proxy; 0 if none).
+    FT   min_ldlt_pivot = FT(0);
 };
 
 // ── Entry function ────────────────────────────────────────────────────────────
@@ -188,6 +199,9 @@ auto discrete_circle_packing_euclidean(
     result.iterations    = nr.iterations;
     result.gradient_norm = nr.grad_inf_norm;
     result.converged     = nr.converged;
+    result.status                  = nr.status;
+    result.sparse_qr_fallback_used = nr.sparse_qr_fallback_used;
+    result.min_ldlt_pivot          = static_cast<FT>(nr.min_ldlt_pivot);
 
     // ── output_uv_map (Phase 8b-Lite extension) ────────────────────────────
     //